Question

Add 4/13 with the multiplicative inverse of 5 1/5​

Answer 1

Answer:

Reciprocal =13/4+26/15

LCM=60

195/60+104/60

=299/60

Answer 2

Question: Add 4/13 with the multiplicative inverse of $5\frac{1}{5}$.

Answer:

The answer is $\frac{169}{338}$.

Step-by-step explanation:

Multiplicative inverse: A number when multiplied by the original number results in 1 is called the multiplicative inverse. More precisely, reciprocal of a number.

Step 1 of 3

Consider the given numbers as follows:

$\frac{4}{13}$ and $5\frac{1}{5}$

Convert the number $5\frac{1}{5}$ from mixed fraction to standard form.

⇒ $5\frac{1}{5} = 5 +\frac{1}{5}$

         $=\frac{25+1}{5}$

         $=\frac{26}{5}$

So, the number in standard form is $26/5$.

Step 2 of 3

Compute the multiplicative inverse of the number $\frac{26}{5}$.

Let the multiplicative inverse be $x$.

Then, using definition

⇒ $x \times \frac{26}{5} =1$

⇒ $x = 1\times \frac{5}{26}$

⇒ $x=\frac{5}{26}$

So, the multiplicative inverse of $\frac{26}{5}$ is $\frac{5}{26}$.

Step 3 of 3

Add the numbers $4/13$ and $5/26$.

⇒ $\frac{4}{13} + \frac{5}{26}=\frac{4\times 26+5\times 13}{(13)(26)}$

Simplify as follows:

$\frac{4}{13} + \frac{5}{26}=\frac{104+65}{338}$

           $=\frac{169}{338}$

Therefore, the final answer is $\frac{169}{338}$.

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